ELEMENTARY ALGEBRA - MWCC

ELEMENTARY ALGEBRA

Overview

The Elementary Algebra section of ACCUPLACER contains 12 multiple choice Algebra questions

that are similar to material seen in a Pre-Algebra or Algebra I pre-college course. A calculator is

provided by the computer on questions where its use would be beneficial. On other questions,

solving the problem using scratch paper may be necessary. Expect to see the following concepts

covered on this portion of the test:

?

??Operations with integers and rational numbers, computation with integers and negative

rational numbers, absolute values, and ordering are included.

??Operations with algebraic expressions that must be solved using simple formulas and

expressions, adding and subtracting monomials and polynomials, multiplying and dividing

monomials and polynomials, positive rational roots and exponents, simplifying algebraic

fractions, and factoring.

??Operations that require solving equations, inequalities, and word problems, solving linear

equations and inequalities, using factoring to solve quadratic equations, solving word problems

and written phrases using algebraic concepts, and geometric reasoning and graphing.

Testing Tips

??Use resources provided such as scratch paper or the calculator to solve the

problem. DO NOT attempt to only solve problems in your head.

??Start the solving process by writing down the formula or mathematic rule

associated with solving the particular problem.

??Put your answer back into the original problem to confirm that your answer is correct.

??Make an educated guess if you are unsure of the answer.

Algebra Tips

Test takers should be familiar with the following concepts. For specific practice exercises using

these concepts, please utilize the resources listed at the end of this guide.

Understanding a number line

Adding and subtracting negative numbers

Using exponents

Finding a square root

Writing algebraic expressions

Using parentheses in algebraic expressions

Evaluating formulas

Multiplying binomials

Using proportions to solve problems

Combining like terms

Evaluating expressions

Solving linear equations

Solving equations

Practice Questions

Order of Operations

1. 3?72

3. 42 ???2

(4 ????2

2. 3 ??2?5??????7?

Please note: Multiplication signs

may take the form of an x, *, or ??

1.3.17

Scientific Notation

Write the following in Scientific Notation. Write in expanded form.

1. 0.0000000000523

2. 6.02?1011

Simplify. Write answers in scientific notation.

?

??5?10 ??

1. 3?103

2. 6 ?109

3?104

6

Substitution

Find each value if x ??3, y ???4, and z ??2.

2. 5x ?z?

xy

1. xy z??4z

Linear equations in one variable

Solve the following for x.

2. 50??x ???3x??2????0

1 . 6x??48??6

Formulas

1. Solve PV ??nRT for T.

2. Solve y ??hx??4xfor x.

Word Problems

1. One number is 5 more than twice another number. The sum of the numbers is 35.

Find the numbers.

2. Sheila bought burgers and fries for her children and some friends. The burgers cost

$2.05 each and the fries are $.85 each. She bought a total of 14 items, for a total

cost of $19.10. How many of each did she buy?

Inequalities

Solve and graph on the number line.

1. 2x?7 ??3

2. 3?x ??4????x ?1?????12

Exponents & Polynomials

Simplify and write answers with positive exponents.

1. ?3x2 ?5x ?6???5x2 ?4x? 4???

?

2. 24x4 ??32x3 ??16x2

8x2

3. ? 5a ??6??

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Factoring

1. x2 ?5x ?6

3. 4x2 ?36 ?? ?

?2. 2x2 ??4x?16

?

?

?

4. 49y2 ?84y ?36?

Quadratic Equations

Solve:

1. 4a2 ??9a??2 ??0

2. ?3x??2?2??16?

Rational Expressions

Perform the following operations and simplify where possible. If given an equation,

solve for the variable.

1.

4

?? 3a

2a ?2

a2 ? a

2.

?

Graphing

16?x2 ??? x2?2x?8?

x2?2x?8

4?x2?

Graph each equation on the coordinate axis.

1.

2.

3.

4.

3x?2y = 6

x ???3

y ??2

y ? -2x + 5

3

Systems of Equations

Solve the following systems of equations.

2x ?3y ???1 2

1. x ?2y ???9

?

Radicals

{

2.

2x? 3y ???4

y??? 2x ?4

{

Simplify the following using the rules of radicals (rationalize denominators). All

variables represent positive numbers.

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Answers

Order of Operations

1. 147

Rule 1: Simplify all operations inside parentheses.

Rule 2: Simplify all exponents, working from left to right.

2. 3 ??2?5?????7 ??3 ??10??7 ??13??7 ??6

3. -9

Rule 3: Perform all multiplications and divisions, left to right.

Rule 4: Perform all additions and subtractions, left to right.

To help remember the order of operations, use the mnemonic

To help remember the order of operations, use the mnemonic

PEMDAS, which stands for Please Excuse My Dear Aunt Sally

(Parentheses, Exponents, Multiplication & Division, Addition &

Subtraction).

Scientific Notation

All numbers in scientific notation have the following form:

Nonzero digit. Rest of number ?10power.

1. 0.0000000000523? 5.23? 10? ????

?

???

2. 602,000,000,000

Substitution

1. xyz -4z = (3)(-4)(2) -4(2) = -24-8=-32

2.

5? ??

??

=

5(3) ?(2)

(3)(?4)

=

125?2

?12

=

123

?12

=?

123

12

=?

41

4

Linear equations in one variable

Formulas?

1.3.17

Word Problems

1. Let ¡°one number¡± =2x + 5 if we let ¡°x¡± = ¡°another number¡± Remember, sum means to add.

There for the two numbers ¡° 2x + 5¡± and ¡°x¡± must add up to 35. So let (2x + 5) + (x) = 35

therefore x = 10 which is ¡°another number.¡± 2x + 5 = 25 which is ¡°one number.¡± So the

numbers are 10 and 25.

2. Let x = the number of burgers. Since ther are only 14 items, the rest of the items, 14 ¨C x,

must = the number of fries. To get the total amount of money spent, multiply the number of

items by the cost of the item. 2.05 x = the total dollars spent on burgers and .85 (14 ¨C x) =

the total dollars spent on fries. The equation is: 2.05x + .85 (14 ¨C x) = 19.10. Solving the

equation, x = 6.

Hence, she bought 6 burgers and 8 fries.

Inequalities

Solve inequalities the same as equations with one exception. When both sides are multiplied or

divided by a negative number, remember to switch the direction of the inequality. Graph a

closed circle if the number is included and an open circle if the number is NOT part of the

solution.

Exponents & Polynomials

Factoring

Steps to factoring, the FOIL method:

1. Always factor out the Greatest Common Factor (if possible).

2. Factor the first and last term.

3. Figure out the middle term by checking combinations of the Inner and Outer terms.

1. x2 ?5x??6 ???x ??6??x ?1?, to check, multiply back using FOIL method

2. 2x2 ??4x?16? 2(x2 ??2x?8)?? 2(x- 2) (x ??4)

1.3.17

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